Question

a flower bed is in the shape of a rectangle with the semicircle if its longer side. if the dimensions of the rectangle is 126 m by 80 m . find its perimeter and area​

Answer 1

Given:

• Length = 126m
• Breadth = 80m

Find:

• Area and the Perimeter of the flower bed.

Solution:

Here,

we, observe from the given fig. that

$\sf Diameter \: of \: semi - circle = 126m$

$\sf So, \: radius \: of \: semi - circle = \dfrac{d}{2} = \dfrac{126}{2}$

$\sf radius \: of \: semi - circle =\dfrac{\cancel{126}}{\cancel{2}} = 63m$

$\underline{\boxed{\sf radius \: of \: semi - circle =63m}}$

Now,

we, know that

$\underline{\boxed{\sf perimeter \: of \: semi - circle = \pi r}}$

where,

• π = $\frac{22}{7}$
• r = 63m

So,

$\sf\to perimeter \: of \: semi - circle = \pi r$

$\sf\to perimeter \: of \: semi - circle = \frac{22}{7} \times 63$

$\sf\to perimeter \: of \: semi - circle = \frac{22}{\cancel{7}} \times\cancel{63}$

$\underline{\boxed{\sf\to perimeter \: of \: semi - circle = 22 \times 9 = 198m}}$

Now, perimeter of the flower bed

= Perimeter of semi-circle + Length + 2×(Breadth)

where,

• Length = 126m
• Breadth = 80m
• Perimeter of semi-circle = 198m

So,

$\sf = 198 + 126 + (2 \times 80)$

$\sf = 198 + 126 + 160$

$\sf = 198 + 286 = 484m$

$\underline{\boxed{\sf Perimeter \: of \: the \: flower \: bed = 484m}}$

Now,

Area of the flower bed

= Area of the semi-circle + Area of the Rectangle

$\sf = \dfrac{1}{2} \times \pi {r}^{2} + (l \times b)$

where,

• Length = 126m
• Breadth = 80m
• π = $\sf\dfrac{22}{7}$
• r = 63m

Now,

$\sf = \dfrac{1}{2} \times \dfrac{22}{7} \times {(63)}^{2} + (126\times 80)$

$\sf =6237 + 10080$

$\sf =16317 {m}^{2}$

$\underline{\boxed{\sf area\: of \: the \: flower \: bed = 16317 {m}^{2} }}$

Hence, The Perimeter of the flower bed will be 484m

and the Area of the flower bed will be 16317m²

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